Radio waves in the ionosphere: Propagation, generation and detection

Radio Waves in the Ionosphere:

Propagation, Generation, and Detection

T. D. C AROZZI

Swedish Institute of Space Physics, Uppsala Division S-752 21 Uppsala, Sweden

Doctoral thesis at Uppsala University

IRF Scientific Report 272 August 2000

Printed in Sweden Swedish Institute of Space Physics

Kiruna 2000 ISSN 0284-1703

Dissertation for the Degree of Doctor of Technology in Space Physics pre- sented at Uppsala University in 2000

ABSTRACT

Carozzi, T.D., 2000, Radio Waves in the Ionosphere: Propagation, Generation and Detection. Swedish Institute of Space Physics, IRF Scientific Report 272, 32 pp. Uppsala. ISSN 0284-1703

We discuss various topics concerning the propagation, generation, and detec- tion of high-frequency (HF) radio waves in the Earth’s ionosphere. With re- gards to propagation, we derive a full wave Hamiltonian and a polarization evo- lution equation for electromagnetic waves in a cold, stratified magnetoplasma.

With regards to generation, we will be concerned with three experiments con- ducted at the ionosphere- radio wave interaction research facilities at Sura, Rus- sia and Tromsø, Norway. These facilities operate high power HF transmitters that can inject large amplitude electromagnetic waves into the ionosphere and excite numerous nonlinear processes. In an experiment conducted at the Sura facility, we were able to measure the full state of polarization of stimulated electromagnetic emissions for the first time. It is expected that by using the technique developed in this experiment it will be possible to study nonlinear polarization effects on powerful HF pump waves in magnetoplasmas in the fu- ture. In another experiment conducted at the Sura facility, the pump frequency was swept automatically allowing rapid, high-resolution measurements of SEE dependence on pump frequency with minimal variations in ionospheric condi- tions. At the Tromsø facility we discovered by chance a highly variable, pump induced, HF emission that most probably emanated from pump excited spo- radic E. Regarding detection, we have proposed a set of Stokes parameters generalized to three dimension space; and we have used these parameters in an invention to detect the incoming direction of electromagnetic waves of multiple frequencies from a single point measurement.

Tobia Carozzi, Department of Astronomy and Space Physics, Uppsala Univer- sity, P. O. Box 515, S-751 20 Uppsala, Sweden

c Tobia Carozzi, 2000 ISSN 0284-1703

Printed in Sweden by the Swedish Institute of Space Physics, Kiruna, 2000.

Alla memoria del mio amato padre, “Nanni” Carozzi . . . och till Mamma

The following dissertation concerning the Trinity, as the reader ought to be informed, has been written in order to guard against the sophistries of those who disdain to begin with faith, and are deceived by a crude and perverse love of reason.

St. Augustine of Hippo,

On the Trinity

This thesis is based on the following papers, which will be referred to in the text with a capital “P” and a Roman numeral:

P-I Parameters characterizing electromagnetic wave polarization T. D. Carozzi, R. Karlsson, and J. Bergman

Phys. Rev. E 61, 2 (2000).

P-II Full Polarimetry Measurements of SEE. First Results

T. D. Carozzi, B. Thid´e, T. B. Leyser, G. Komrakov, V. Frolov, S. Grach and E. Sergeev

Submitted to Journal of Geophysical Research, April 2000.

P-III High resolution measurements of SEE dependence on pump

T. D. Carozzi, B. Thid´e, T. B. Leyser, M. Holz, G. Komrakov, V. Frolov, S. Grach and E. Sergeev

Submitted to Journal of Geophysical Research, (2000).

P-IV Observations of nonstationary radio emission induced by a

T. D. Carozzi, T. B. Leyser, J-O. Hall, and M. T. Rietveld Submitted to Geophysical Research Letters, (2000).

P-V Hamiltonian formulation of radio wave propagation in a cold,

T. D. Carozzi

IRF Scientific Report 268, (2000).

P-VI Evolution equations for radio wave polarization in a cold, strat-

T. D. Carozzi

IRF Scientific Report 271, (2000).

P-VII Method and system for obtaining direction of an electromag-

J. Bergman, T. Carozzi, and R. Karlsson

Swedish Patent Publication No. 512 219 (2000), (International Patent Publication WO 99/66341).

This manuscript was typeset in L^ATEX 2¡ on a dual 500 MHz Pentium Pro workstation running Linux and printed on an HP LaserJet 5000GN printer.

CONTENTS

1 I

– How a few waves sparked a technological tsunami 1

2 E

’

I

– The Stage 3

1 Discovery of an “Electrically Conducting Region” Around the Earth . . . . 3 2 A Modern View . . . . 4

3 H

– The Actors 6

1 Theoretical Research . . . . 6

4 P

– The Masks of the Actors 8

5 SEE – The Intrigue 11

1 Short history of HF ionospheric modification experiments . . . 11 2 Stimulated Electromagnetic Emissions (SEE) . . . . 12 3 Environmental aspects . . . . 16 6 C

O

– How they all lived happily ever af-

ter. . . 18

7 P

S

20

A

23

B

25

CHAPTER 1

I NTRODUCTION – How a few waves sparked a technological tsunami

It has been said of our time that it is the age of information and global com- munication. If this is so, it all started in St. John’s, Canada a cold and snowy December day in 1901, just less than 100 years ago . . .

“Shortly before midday I placed the single earphone to my ear and started listening. The receiver on the table before me was very crude – a few coils and condensers and a coherer – no valves, no amplifiers, not even a crystal. But I was at last on the point of putting the correctness of all my beliefs to test. The answer came at 12:30 when I heard, faintly but distinctly, pip-pip-pip. I handed the phone to Kemp: ”Can you hear anything?” I asked. ”Yes,”

he said. ”The letter S.” He could hear it. I knew then that all my anticipations had been justified. The electric waves sent out into space from Poldhu had traversed the Atlantic – the distance, enormous as it seemed then, of 1,700 miles – unimpeded by the curvature of the earth. The result meant much more to me than the mere successful realization of an experiment. As Sir Oliver Lodge has stated, it was an epoch in history. I now felt for the first time absolutely certain that the day would come when mankind would be able to send messages without wires not only across the Atlantic but between the farthermost ends of the earth.”

These are the words of Guglielmo Marconi (1874–1937) the first man to communicate wirelessly over the Atlantic. Radio, the term we now use for this phenomena, was coined just following year in 1903. The technological impact of this invention are still with us today and can only increase in the fu- ture. Somewhat incredibly, physists are still today at work trying to understand various aspects of radio. And to the human mind this marvelous invention, in which voices from the other side of the Earth resound inside a box, will always be a form of scientific magic.

Not only is radio the starting point of the modern communications society, it is also the central theme of my thesis. This doctoral dissertation in space

1It seems even Albert Einstein was of this opinion when he said “One ought to be ashamed to make use of the wonders of science embodied in a radio set, the while appreciating them as little as a cow appreciates the botanical marvels in the plants she munches.”

Figure 1.1: Guiliemo Marconi in 1901 during his classic experiment with transatlantic radio. Note the radio equipment on the table and the empty food tins in the cupboard.

Alas, little has changed in experimental radio research.

physics, which will be summarized in the pages to follow, deals with various topics related to radio waves in the ionosphere. In particular, it deals with some extensions of radio wave propagation theory, some experimental find- ings on the generation of secondary radio waves induced by large amplitude radio waves in the ionosphere, and some work on the detection, identification, and characterization of radio waves in terms of generalized polarization con- cepts. In writing this summary, I have used the metaphor of a theater play:

the ionosphere is the stage, the radio waves are the actors, wave polarization is the masks or costumes of actors, and the intrigue is the research on the in- duced radio waves from the ionosphere known as stimulated electromagnetic emissions or SEE. An attempt at presenting and explaining the popular science background on each of these concepts will be made. Where it is appropriate, the contributions of the papers which constitute this thesis, will be presented.

And along the way, we will be guided by the spirit of Marconi. This summary

closes by discussing some views on the future or continuations of the work

found in the thesis. Finally, a concise summary over each of the thesis papers

is given.

CHAPTER 2

E ARTH ’ S I ONOSPHERE – The Stage

1 Discovery of an “Electrically Conducting Region” Around the Earth

Marconi’s classic experiment across the Atlantic was not the first time wireless transmission had been demonstrated. There were successful attempts at radio communication by Marconi himself before 1901, and there are even claims that the Russian Popov developed the radio before Marconi. So why then was this achievement so important that it overshadowed previously successful attempts and what was the motivation to award him with a Nobel prize in 1909? Simply because virtually no one believed radio signals could be transmitted that far. It was a common understanding that Hertzian waves, as radio waves were called at the time after their discoverer H. Hertz, could only travel in straight lines or line-of-sight paths. Due to the curvature of the Earth, it was therefore only pos- sible to transmit a distance of no more than 100 km. Many of the great minds of the day deemed Marconi’s vision of global communication as ludicrous; and in anyway, what would it be good for? In his final years, when Marconi received in Australia a radio signal which had traveled half way across the Earth from England, he had at last fulfilled his dream, and in the process brought the world closer together.

At the same moment Marconi’s trans-atlantic experiment had proven suc- cessful, a new field of science was born. Clearly it was necessary to explain how a radio wave could get from Poldhu, Cornwall to St. Johns, Newfound- land. Most the great physicists of the time simply suggested that a special type of electromagnetic wave was involved that followed the curvature of Earth.

The boldest proposition to solve this problem came in 1902 from American

engineer A. Kennelly and British physicist O. Heaviside. They suggested that

an electrically conducting region in the atmosphere could explain Marconi’s

results. This came at a time when the region above the atmosphere was as-

sumed to be a perfect vacuum, namely outer space, long before rockets could

detect in situ what was out there. It was not until 1925, through the work of

E. V. Appleton, M. A. F. Barnett, G. Breit, and M. A. Tuve using radio tech-

niques and theory, that the region now known as the ionosphere was proven

unambiguously.

Figure 2.1: The Earth’s radio ionosphere.

2 A Modern View

An illustration of the Earth’s radio ionosphere, as it is known today, is shown in Figure 2.1. The most important and defining feature of the ionosphere is the presence of ionized gas. In the ionosphere, the amount of ionized gas compared to neutral gas becomes sufficiently large to radically change the properties of the whole mixture, to the point that it no longer behaves as a pure gas. It is reasonable to consider such a condition as the fourth state of matter; and this state was given the name plasma by Langmuir during the 1920s. Since the ionosphere can be seen as an enormous naturally occurring plasma volume, ionospheric research and plasma physics are naturally closely intertwined.

The ionosphere maybe the closest naturally occurring example of a plasma, but as plasma, it is not unique. In fact, the major part of the visible matter in the universe is in a plasma state. The study of our ionosphere has therefore enormous value in our understanding of the rest of plasma universe.

The plasma roof of the Earth, or ionosphere, is not simply idly floating above our heads: it needs to be constantly replenished. The Earth is con- tinuously bombarded from outer space by various types of radiation. Some of the radiation has such high energy that it may strike out electrons orbiting gas atoms in the atmosphere and thereby creating ions and free electrons in the process. The number of free electrons per unit volume is known as the plasma density. Roughly put, the fundamental differences in the various kinds of such ionizing radiation results in a layering of the ionosphere in altitude.

On average, the plasma density as a function of altitude becomes significant somewhere below 90 km and the region up to this height is called the D region.











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range of 130–1000 km, which is known as the F region. After the F region, the

plasma density drops as one approaches the outer regions the Earth’s plasma

environment known as the magnetosphere.

CHAPTER 3

H IGH FREQUENCY RADIO WAVES – The Actors

Today, a hundred years after man made radio waves were first evidently passed through a plasma, we have a good understanding of how radio waves propa- gate. We are now aware of the different modes of propagation, where the wave reflect, how their amplitude swells as they reflect and many other things. In fact, ionospheric radio on the whole is straight forward engineering nowadays.

This does not mean, however, that few questions remain on radio ionosphere.

And neither does it mean that new theoretical understandings of radio wave propagation are not called for.

1 Theoretical Research

Traditionally, the theory of radio wave propagation in stratified, magnetized plasmas is discussed in terms of a linear fourth order ordinary differential equa- tion, which are derived from Maxwell’s equations together with an appropriate permittivity tensor. In P-V, I show how it is possible to construct a Hamil- ton formalism which reproduces the fundamental differential equations. This Hamiltonian formalism is not to be confused with the Hamiltonian formula- tion used ray tracing or geometrical optics. In ray tracing one obtains a set of canonical equations for the path of the ray and its refractive index vector.

The Hamiltonian in this case is a suitable dispersion relation. The Hamiltonian introduced in P-V is not a dispersion relation and furthermore it generates the full wave equations in contrast to the approximate eikonal equations.

Another very different approach to radio wave propagation theory is to study the evolution of bilinear forms of the electric and magnetic field com- ponents. These bilinear forms are in part related to electromagnetic energy and electromagnetic energy flux, but also to electromagnetic wave polariza- tion. The formulation used in P-VI is to derive a system of equations which govern the evolution of the polarization into a magnetoplasma gradient.

The formalisms of radio wave propagation summarized here were devel-

oped in the interest of providing a starting point for the study of nonlinear

polarization effects of large amplitude radio waves in a magnetoplasma. The

field of nonlinear interaction between radio wave and plasmas is a very active

field in radio/plasma research. We will have more to say on one aspect of this

research later, but before we do this, we have more to say on the radio waves

themselves, namely how they are to be characterized.

CHAPTER 4

P OLARIZATION – The Masks of the Actors

Long before Hertz discovered the radio wave, scientists were doing research on electromagnetic wave propagation under the more familiar name of optics.

It soon became apparent that light, unlike sound waves or water, could not be characterized fully only by its amplitude or intensity. Certain characteristics of light invisible to the human eye must exist in order to explain experimental results. The most famous characterization of light was due to Stokes. He in- troduced four real quantities I

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It can thought of as the phase space of quasi-monochromatic waves. The poles of the sphere, represent circularly polarized waves, while the equator represents linearly po- larized waves. The meridians represent different tilt angles of the polarization ellipse.

Finally, the radial dimension represents the degree of polarized or coherency of the wave: the surface of the sphere represents states of pure waves while the origin rep- resents the completely random or unpolarized state. This particular Poincar´e sphere has been drawn to represent radio waves measured on the ground and therefore the handedness is with respect to nadir and the tilt angle is with respect to the North-South magnetic meridian.

In other words, the Stokes parameters are the Pauli spin matrix components of

the coherency matrix of the transverse electric field. Furthermore, it is well

known that the Pauli spin matrices are a representation of the generators of the

SU(2) group. A natural extension of the Stokes parameters in this context is

to consider the outer product of the entire electric field and its conjugate, and

to expand this outer product using the generators of the SU(3) group. This is

precisely what was carried out in paper P-I.

CHAPTER 5

SEE – The Intrigue

1 Short history of HF ionospheric modification experiments

One of the most incredible aspects of Marconi’s 1901 experiments was that they were performed without the aid of amplification! Soon vacuum tubes appeared and the output power of radio transmitters could be increased to im- prove reception quality. The increase in transmitter power grew to the point where in 1930 the so called Luxemburg effect was observed; a phenomena which is most readily explained in terms of nonlinearity. A Dutch scientist was listening to the signal from a transmitter located in Berom ¨unster but was sur- prised to hear at the same time a different radio station located in Luxemburg.

Compared to our everyday experience of sound this is a truly surprising effect:

imagine listening to a note on a violin which suddenly is shifted in tone as a powerful cello note is played. Phenomena such as these are in principle always possible to achieve if one of the waves involved, called the pump, is powerful enough to heat or significantly stress the medium it passes through. When the other wave, called the probe, passes through the region stressed by the pump, the probe will pickup the modulation of the pump. In this way, information has passed from the pump to the probe through the changes induced in medium by the pump.

The effects of powerful radio waves on the ionosphere was eventually stud- ied more systematically during the 1970s when dedicated radio facilities were constructed. These facilities were originally called heaters since they were built with the anticipation that they would increase the electron temperatures in the ionosphere above them. Basically a heater is not very much more than a commercial radio transmitter in the high frequency (HF) range. Their antennas, however, typically transmit vertical beams incident on the ionosphere. One can typically modulate the beam, choose it’s polarity and sometimes frequency and other parameters of scientific interest.

One of the first modern heaters was built in Platteville in the United States,

1970. Soon it was found that heaters could do more than just heat the iono-

spheric plasma. It was observed that they could induce a number surprising

effects such as the parametric decay instability and the oscillating two stream

instability. Very soon after Platteville, heaters were built around the world at

such diverse locations as Arecibo, Puerto Rico; Nizhny Novgorod, Russia (for-

Figure 5.1: The Sura heating facility near Vasil’Sursk, Russia.

merly Gorky, Sovjet); and Tromsø, Norway. Although these facilities are now highly venerable, they are still in active use today and continue to generate new discoveries and scientific output.

Two of the papers included in this thesis are based on observations made in 1998 at the Sura facility near the small village of Vasil’Sursk, 100 km east of Nizhny Novgorod, Russia. A photograph of part of the antenna is shown in Figure 5.1. Another paper was made in 1999 at the Ramfjordsmoen facility locate. It is shown in Figure 5.2.

2 Stimulated Electromagnetic Emissions (SEE)

Almost 20 years ago, it was discovered that not only can a powerful radio wave excite plasma waves and processes in the ionosphere, the HF perturbed plasma could reradiate electromagnetic waves detectable on the ground. These induced secondary radio waves, discovered by B. Thid´e, were later given the name stimulated electromagnetic emissions or SEE. In Figure 5.3, one can see one of the very first SEE spectra. The picture is of the display of a Hewlett- Packard spectrum analyzer which, at the time of the photograph, was posi- tioned in a valley adjacent to the valley where the Tromsø transmitter is lo- cated. The Tromsø transmitter, being essentially monochromatic, appears on the spectrum analyzer display as a line spectrum. As one can see for oneself, not only is the transmitter signal visible in the middle of the display, but con- siderable energy exists in the sidebands, especially the lower sideband.

Theoretically, the problem of how plasma can, under certain conditions, ra-

diate electromagnetic waves is of fundamental importance, involving such phe-

nomena as solar bursts, auroral kilometric radiation, Jovian emissions and SEE.

Figure 5.2: The EISCAT heating facility near Tromsø, Norway.

Figure 5.3: Photography of the display of a spectrum-analyzer showing one of the very first measurements of SEE.

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14

Despite their importance, these processes are still poorly understood. What makes SEE so interesting is that it is possible to study such phenomena under controlled and repeatable conditions.

During the final afternoon of an experimental campaign in 1998 at the Sura, HF pump facility in Vasil’Sursk, I was given the opportunity to perform two experiments related to SEE. The first was a very simple experiment: the pump was swept over a frequency range centered on a gyroharmonic. In the second experiment, the complete state of polarization of steady state SEE was mea- sured.

The most important parameter determining the SEE features is the prox- imity of the pump frequency to an electron cyclotron harmonic. The number of different spectral signatures of SEE is most bewildering until the spectra are organized according to pump frequency and an order is perceived. The sweep experiment discussed in P-III clearly shows how SEE spectra vary with pump frequency in the particularly interesting frequency interval which in- cludes the fourth gyroharmonic. It was anticipated that the pump sweep exper- iment would not give any information that was not already known. However, it eventually became clear that the greatly improved frequency resolution and the ability to reduce the detrimental effects of ionospheric variability made it pos- sible to make new discoveries. For instance, comparison of the DM resonance with the 2DM resonance curve and also the 3DM resonance curve provide ev- idence for the cascade model for DM generation. Also, it was discovered that there are weak BUM emissions below the BUM cutoff, a region where current BUM generation models predict that there should not be any emissions. Judg- ing by the results of the pump sweep experiment, it could be very useful to repeat the technique.

The importance of wave modality for SEE generation has been known ever since their discovery. It is observed that only O-mode transmission induce SEE and that the SEE themselves were mainly O-mode. Of course the modality is just one aspect of the more general concept, state of polarization (SOP). In the last experiment conducted during 1998 SEE campaign, I attempted to measure the full SOP of steady state SEE. The technique employed was to simultane- ously measure both the North–South and the East–West aligned segments of the Sura facilities receiving antenna using two synchronized, digital, HF sam- pling units. After the actual experiment, the digital data needed to be processed to derive a spectrum for four quantities which characterize the SOP and are re- lated to the four Stokes parameters. The results were conveniently visualized using a specially designed graphical aid based on the Poincar´e sphere. It was found that the SEE did not have a trivial SOP, i.e. they were not simply left- hand circularly polarized. In fact the ellipticity of the BUM tended from LHP to linearity for lower and lower frequency values within the BUM. This may either be an indication of X-mode contribution or of an increase in the oblique- ness of the incoming emissions perhaps orthogonal to the local magnetic field.

It was also found that there were noticeable differences in the SOP depending

on whether the pump was slightly above or below the gyroharmonic. Finally, it

was interesting to find that the received pump wave, which upon transmission

had been almost pure LCP or O-mode, was found to be RHP during steady state conditions.

After continuous wave (CW) transmission of an HF pump on the order of a minute, the spectrum of the SEE will attain so called steady state. This means that the SEE spectrum changes only gradually on a time scale of min- utes corresponding to natural variations in the ionosphere. It was therefore very surprising to observe, during an experimental campaign at Tromsø heating fa- cility, pump induced emissions which did not exhibit steady state. They were only clearly recognized as a systematic effect when the received HF signals were shown in terms of spectrograms. By contrast, when the received HF sig- nals were viewed in terms of instantaneous spectra they were at first incorrectly interpreted as interference. The emissions, which we called high frequency, in- duced, dynamic emissions (HIDE), appeared on the spectrogram as multiple streaks which at times moved together, ascending or descending in frequency.

An individual streak could come into existence within a fraction of a second, could last several seconds and then vanish in less than a second. The emissions were clearly induced by the heater as was evidenced by their almost immediate appearance and disappearance as the pump turned on and off respectively. The ocean was mainly O-mode polarized and induced during O-mode pumping just like SEE but they were also observed during X-mode transmission unlike SEE.

A convincing explanation for the ocean has yet to be suggested.

3 Environmental aspects

Clearly, radio has had a enormously beneficial effect on our society and the future of wireless communication and other application is to say the least enor- mous. But as with all technological advances, there may be side effects. It is obvious that much has changed in the 100 years since the simple radio ex- periment of Marconi. From the ground we have TV, radio, mobile telephones, weather radars, navigational radars; and from space we have telemetry sys- tems, satellite TV, radio, microwave remote sensing and so on. These radio based systems are expanding rapidly in both number and radiated power and very soon we will see ambitious space based projects such as global wireless internet and personal visual-audio telephony.

Now most people are familiar with the ozone layer and its role as protec- tive blanket, shielding delicate ecosystems from dangerous ultraviolet radiation from the sun. Regrettably, fewer people are familiar with the ionosphere and its analogous role in protecting Earth from dangerous forms of radiation. In fact, the ionosphere is the direct result of ionizing radiation impacting on our neutral atmosphere.

As the radio stress on the Earth’s ionosphere increases and society’s de-

pendence on radio based systems grows, a better scientific understanding of

the effects of high power radio waves on the ionosphere would be highly use-

ful. And even though some have been critical of the environmental impact of

ionospheric modification facilities in the past, these facilities are after all the

best controlled source for studying the environmental aspects of radio. Clearly

it is wiser to know in advance what one can regret in the future.

CHAPTER 6

C ONCLUSION AND O UTLOOK – How they all lived happily ever after. . .

Much on the work in this thesis has more the nature of starting points rather than closing point for research. Several techniques have been developed here, such the HF polarimetry technique, the direction finding technique, and the pump sweep technique, which will hopefully prove fruitful in future experi- ments in radio wave–ionospheric interaction experiments. As far as future ex- periments are concerned, there are too many for one lifetime to suffice, there- fore it may be wise to mention a few here.

Concerning the pump sweep, it would ultimately be very interesting to sweep the pump through the entire ionosphere, as this would give a catalogue of all the pump frequency dependent HF emissions in the ionosphere. It would be interesting to further explore the emence possibilities of nonmonochromatic pump waves of which the pump sweep is an example. For instance, at the Tromsø facility, we recently attempted an psuedo-incoherent pump wave ex- periment in which the coherency of the transmitted signal could be varied para- metrically. This could be used to explore the dependence of nonlinear plasma processes on the coherency of the pump.

The HF polarimetry technique was intended to be used to measure nonlin- ear polarization effects on large amplitude waves in plasmas. In future it would be very interesting to try to observe the radio–plasma analogues of the Kerr ef- fect or the inverse Faraday effect in ionospheric pump experiments and a host of other self-action or pump-probe interaction polarization effects. Furthre- more a simple search for induced X-mode emissions is duely called for. Finally an extension of the single point HF polarimetry to include the full advantages interferometry could have enormous potential.

It would also be valuble to continue work on nonlinear polarization effects in radio wave–plasma interactions, which to my mind is well developed in optics but not as well know in nonlinear plasma study. In this direction, gener- alizations of the polarization concept to higher orders of correlation should be investigated, such as

E

E

E

œ

which can directly give signatures of three-way

interactions. Some work is already underway such as a covariant formula-

tion of the concept of polarization. Explicit characterisation of all well-known

plasma waves in terms of these generalized polarization parameters should be

carried out in the future.

Finally, the accidental “discovery” of emissions induced in sporadic E of a nonstationary nature should also be followed up. Combined experiments with incoherent and coherent radars would be of great value in this exploration.

Alas, only time can tell which of these topics will see the light of day. . .

CHAPTER 7

P APER S UMMARIES

P-I. Parameters characterizing electromagnetic wave polariza- tion

The Stokes parameters characterize the properties of quasi-monochromatic, electromagnetic plane waves. In P-I a generalization of the Stokes parameters is presented which includes all three components of the electric or magnetic field and in addition allows for wide-band waves. The generalization is based on the decomposition of the full three-dimensional spectral correlation matrix in terms of base matrices representing generators of the SU(3) group.

P-II. Full Polarimetry Measurements of SEE. First Results

Nonlinear effects in ionospheric plasma caused by high power radio waves has

been known since the 1930s. By controlled experiments it has been realized

that large amplitude radio waves can excite secondary electromagnetic waves

at frequencies different from that of the mother wave. One class of such in-

duced secondary emissions, in the high-frequency regime, are the stimulated

electromagnetic emissions (SEE). In the study of their properties, the focus in

the past has been to analyze the time development of the power of SEE spectra

under various conditions. In this paper, we develop a theory and a technique to

detect the full state-of-polarization (SOP) of SEE, of the power is but one out

of a total of four parameters. The technique was used in an experiment con-

ducted at the Sura HF wave-ionosphere interaction facility. The results show

that the SEE could have distinguishing SOP properties. In the future, other ex-

periments could employ this technique to study nonlinear polarization effects

in large amplitude electromagnetic wave in a magnetoplasma as a complement

to the traditional spectral analysis.

P-III. High resolution measurements of SEE dependence on pump frequencies close to the fourth electron cyclotron harmonic

It is well established that spectra of stimulated electromagnetic emissions are extremely sensitive to the pump frequencies proximity to electron gyroharmon- ics. Unfortunately, the detailed study of this dependence has been limited to manually tuning and retuning the pump, which can take minutes and is only feasible to perform for a maximum of a few tens of frequency increments.

This paper deals with an experiment in which we utilized an automated pump frequency stepping procedure which resulted in data of such high resolution and minimal ionospheric variation that new discoveries on the generation of SEE were made. For instance, we found evidence for a cascade model to ex- plain the generation of the downshifted maximum (DM) feature of the SEE. We also observed emissions associated with the broad upshifted maximum (BUM) but were below the supposed cut-off frequency for the BUM. This technique could be used at high gyroharmonics to resolve the DM intensity minimum to determine if it actually consists of two minima as predicted by some theories.

P-IV. Observations of nonstationary radio emission induced by a powerful high-frequency radio wave incident on sporadic E

By accident, during a campaign focusing on the measurement of SEE at the Tromsø heating facility in November 1999, we observed very unusual pump induced HF emission. The intermittent, highly variable nature of this emission is very unlike traditional SEE, which are typically highly stable and eventually exhibit a steady state. The emission bears a striking resemblance to naturally occurring auroral roar emission and also to zebra-pattern fine structure of solar bursts. Analysis of the elapsed time between ground wave reception and sky wave reception revealed that the emissions were probably emanating from ex- cited sporadic E. This would then be the first direct observation of HF emission generated in sporadic E.

P-V. Hamiltonian formulation of radio wave propagation in a cold, stratified magnetoplasma

The theory of low power radio waves in the ionosphere can be roughly bro-

ken into two categories: ray tracing, in which one derives wave propagation by

minimizing the phase length of the wave path or full wave solutions, in which

the Maxwells equations are solved directly assuming wave propagation in a

plane stratified cold magnetoplasma. The full wave theory in this case consists

of a fourth order ordinary differential equation in the vertical dimension vari-

able. As it turns out, it is possible to derive a Hamiltonian function, terms of

the horizontal electric and magnetic field components and their adjoints and

the height variable. P-V introduces this Hamiltonian.

P-VI. Evolution equations for radio wave polarization in a cold, stratified magnetoplasma

In this paper, we develop a theory for the evolution of parameters related to the polarization of electromagnetic wave in a cold, stratified magnetoplasma. It is demonstrated that if the proper representation is used, some of the parameters will be conserved under the propagation of the radio wave. This formalism is though to be a starting point for the development of a theory for nonlinear polarization effects in large amplitude radio waves in the ionosphere.

P-VII. Method and system for obtaining direction of an electro- magnetic wave

This paper is a patent describing an apparatus which determines the incidence

direction of an impinging electromagnetic wave. This is done using some basic

properties of electromagnetic radiation. The described system is comparable

to other direction finding techniques such as interferometry or the use of high

gain antennas. The advantage of our technique is that it requires only a single

point measurement, in contrast to interferometry, and it avoids the complexi-

ties involved in using high gain antennas (which requires either a mechanical

angular sweep or a complex multiple antenna arrangement).

Acknowledgements

Space is a big place; but to write a doctor’s thesis in space physics is even bigger. And while it has been said “in space, no one can hear you scream,”

writing a thesis on space physics, you won’t have time to scream, even though you’d probably want to.

This is not to say that the process and ultimate goal was not worthy the substantial effort; and for this there are many people to thank. As a child I always used to wonder why adults during formal occasions would go to such lengths to express there gratitude towards others. I did not see the point then but I certainly do now.

To all the personnel at IRF-U, I am greatful for your help and assistance and I will cherish the final time spent at the place which is now but a chapter in history, namely Lurbo, and of which you are an inseparable part.

To my “Handledare,” Bo Thid´e, I express my gratefulness for the time you spent working with me. Through the years we have been to some of the most desolate places in the world – or so it seems – and these rare situations, which are totally unlike the mundane world, will stay with me forever.

To all my scientist colleagues in the world, I wish to acknowledge the inspi- ration, warmth and experience you have shared with me. This goes especially to my friends in the “wavegroup” corridor, which despite the fact it no longer exists in the material world, surely live on in spirit. And also to my Russian colleagues for the unparalleled experiences made in wondrous Russia and their uniquely genuine brand of friendship.

Above all, I wish to thank two people directly responsible for helping me with my thesis. One is Jan Bergman without whom this thesis would surely not have been what eventually became. The daily discussions with you combined with your friendship were imperative in the completion of this work, and it is only fitting that we end this, our mutual academic endeavor, by defending our theses side by side. And the other is Andrea, which has shown a patience unrivaled in the galaxy. Your untiring help and assistance in big and small was precisely what I needed: tack och stor kram.

Finally, I have dedicated this thesis to memory of my father, Dr. Giovanni

Carozzi, who instilled in his son a fascination for this world and a love for it’s

ineffable beauty, grazie. Och givetvis vill jag tacka ¨aven min k¨ara mor och

systrar.

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